4.

The problem involves solving for the individual work rates of two drivers based on their combined rate and a split-work scenario. By setting up a quadratic equation based on the time taken for each to complete half the job, we find that Driver B takes 30 days to complete the full task alone.

Step-by-step Derivation:
Step 1: Define variables. Let $a$ be the time Driver A takes to complete the job alone and $b$ be the time Driver B takes to complete the job alone. Their rates are $1/a$ and $1/b$ per day.

Step 2: Use the combined work rate. Together they finish in 7.5 days: $\frac{1}{a} + \frac{1}{b} = \frac{1}{7.5} = \frac{2}{15}$.

Step 3: Set up the split-work equation. A does half the job, then B does half the job, totaling 20 days: $\frac{a}{2} + \frac{b}{2} = 20$, which simplifies to $a + b = 40$.

Step 4: Substitute $a = 40 - b$ into the combined rate equation: $\frac{1}{40-b} + \frac{1}{b} = \frac{2}{15}$.

Step 5: Solve for $b$: $\frac{b + (40-b)}{b(40-b)} = \frac{2}{15} \implies \frac{40}{40b - b^2} = \frac{2}{15}$.

Step 6: Cross-multiply: $40 \times 15 = 2(40b - b^2) \implies 600 = 80b - 2b^2 \implies 2b^2 - 80b + 600 = 0$.

Step 7: Simplify the quadratic: $b^2 - 40b + 300 = 0$.

Step 8: Factor the quadratic: $(b - 30)(b - 10) = 0$. Thus, $b = 30$ or $b = 10$.

Step 9: Determine the correct value based on efficiency. If $b = 30$, then $a = 40 - 30 = 10$. If $b = 10$, then $a = 30$. The problem states A is more efficient than B, meaning A takes less time than B ($a < b$). Therefore, $a = 10$ and $b = 30$.